Interspecific allometry of bone dimensions: A review of the theoretical models

A fascinating problem in biological scaling is the variation of long-bone length (or diameter) Y with body mass M in mammals, birds, and other vertebrates. It turns out that Y and M are related by a power law, namely Y=Y₀M^b, where Y₀ is a constant and b is the so-called allometric exponent. The origin of these power laws is still unclear because, in general, biological laws do not follow from physical ones in a simple manner.Here we make a historical review of this subject, summarizing the main experimental papers as well as discussing the main theoretical proposals. Long-bone allometry seems to be determined by the need to resist the particular loads applied to each bone in each taxon. Experimental measurements of in vivo stresses have found that mammalian long bones are subjected mainly to compression and bending, while avian wing-bones and reptilian limb-bones suffer a high degree of torsion. A recent model, based on the hypothesis that mammalian long-bone allometry is determined by compressive and bending loads, was able elucidate several aspects of mammalian limb-bone scaling. However, an explanation for avian and reptilian long-bone allometry is still missing.     

Allometric scaling of countries

As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, and urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than 1) or nearly linear allometric scaling relations with the GDP. Meanwhile, the geographic (arable area, natural resources, etc.), demographic (labor force, military age population, etc.) and transportation-related properties (road length, airports) have significant and sub-linear (the exponent is smaller than 1) allometric scaling relations with area. Several differences of power law relations with respect to the population between countries and cities were pointed out. First, population increases sub-linearly with area in countries. Second, the GDP increases linearly in countries but not super-linearly as in cities. Finally, electricity or oil consumption per capita increases with population faster than cities.     

Broken scaling laws of the transition probabilities from jj to LS coupling transitions

Accurate electromagnetic transition rates between the ground electronic configurations are important in diagnostic studies of planetary nebulae. Based on a “quasi-complete basis” set, we present large-scale multi-configuration Dirac–Fock calculations of the forbidden transition rates within the ground electronic configuration along the nitrogen-like isoelectronic sequence. The broken scaling laws of the transition probabilities from jj to LS coupling transitions are elucidated and found to be extensions of the well-known scaling laws discussed in the single electron case. The equivalent oscillator strength is very large for ions in high-Z regions and should play a crucial role in the cooling mechanism in astrophysics.     

Effective temperature and scaling laws of polarized quantum vortex bundles

An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A∝k−1/2, follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.     

Towards a geometrical classification of statistical conservation laws in turbulent advection

The paper revisits the compressible Kraichnan model of turbulent advection in order to derive explicit quantitative relations between scaling exponents and Lagrangian particle configuration geometry.     

Investigation of scaling laws in frequency-dependent minor hysteresis loops for ferromagnetic steels

Scaling laws in dynamical magnetic minor hysteresis loops have been investigated in the magnetizing frequency range of 0.05-300 Hz for various steels including Cr-Mo-V steel subjected to creep, cold rolled steels, and plastically deformed Ni. Although scaling laws in the medium magnetization range found previously fail in the high magnetization frequency regime owing to a significant contribution of eddy currents, a scaling power law of the relation between remanence and remanence work of minor loops, associated with a constant exponent of approximately 1.9, holds true in a very low magnetization regime, irrespective of magnetization frequency and investigated materials. The coefficient of the law is proportionally related to Vickers hardness over the wide frequency range. These observations demonstrate that the scaling analysis of dynamical minor loops enables us to evaluate materials degradation in a short measurement time with low measurement field and high sensitivity to defect density.     

The emergence of scaling laws search dynamics in a particle swarm optimization

This paper investigates the search dynamics of a fundamental particle swarm optimization (PSO) algorithm via gathering and analyzing the data of the search area during the optimization process. The PSO algorithm exhibits a distinct performance when optimizing different functions, which induces the emergence of different search dynamics during the optimization process. The simulation results show that the performance is tightly related to the search dynamics which results from the interaction between the PSO algorithm and the landscape of the solved problems. The Lévy type scaling laws search dynamics emerges from the process in which the PSO algorithm shows good performance, while the Brownian dynamics appears after the algorithm has stagnated due to the premature convergence. The Lévy dynamics characterized by a large number of intensive local searches punctuated by long-range transfers is an indicator of good performance, which allows the algorithm to achieve an efficient balance between exploration and exploitation so as to improve the search efficiency.